We performed BD simulations of such a supercoil accumulation based on the dWLC method. In Fig. REF , the relative extension \(z/L\)  almost remains unchanged before 0.6 s while the torque gradually builds up, suggesting that the extended DNA is twisted. The buckling at about 0.6 s marks the starting-point of the phase-coexistence. The buckling transition indicates a competition between pre-plectonemic loops and stretched phase[1]}, [2]}. After 0.6 s, the torque drops and converges as torsional stress on DNA is relieved, indicating the twist is transformed into writhe. These discontinuities have previously been observed in single-molecule experiment[3]}. The coexistence torque \(T_q^{co}\)  remains unchanged when more linking number is injected. Note that multiple plectonemes can co-exist in the process. The representative snapshots are also shown in Fig. REF . The unchanged torque curves or the linearly decreased extension after buckling transition suggest that the process remains quasi-static.
